Advanced plasma tools have been using very high frequency power sources or combination radiofrequency (RF) and direct current (DC) power supplies to advance greater control over the plasma formation process and performance. Recently, for example, capacitively coupled plasma (CCP) reactors have employed dual frequency (DF) power delivery to control the energy and density of the ions and radicals at the surface of a wafer being processed. In such reactors, the effectiveness and the quality of the process being performed depends on the distributions of this energy and of the various particle species in the processing chamber, particularly near the wafer surface. Inductively coupled plasma (ICP) reactors, such as ionized physical vapor deposition (iPVD) reactors, employ combinations of gas and coating material species plus energy introduced from a number of different sources within the geometry of a processing chamber. In these systems, the material and energy distributions that affect the process being performed are reached after initial parameters are established, transient behavior has subsided, and the system has stabilized. However, the physics of this process has not been fully understood and has been the subject of continued theoretical and experimental investigations.
Plasma modeling and numerical simulations play in an important role in understanding plasma behavior in these systems. Modeling and simulation methods can play important roles in the development and optimization of plasma equipment and related plasma processes.
While, in the last decade, computing systems have greatly increased capabilities for numerically modeling complex and robust plasma-chemical systems like etching systems (for example central processing unit (CPU) speed, multi-core architecture, memory resources, and large size data storage capacities), the computational time required for a full numerical simulation is often on the scale of many hours, and in some specific complex cases, can be several days. Most computing systems and software are not yet ready and/or capable for parallel computing for a variety and specific tasks.
For example, even with the simplest plasma model, e.g. inert argon gas with a basic geometry etching system, a computer simulation of the plasma density distribution can take several hours (2-6 hours) to converge if the model includes mutually coupled mass transport equations, heat and energy balance equations, and electromagnetic (EM) wave propagation equations of 100 MHz (i.e. RF cycle on a 10 ns time scale). To generate a full transient solution on a system excited by a lower frequency EM wave would require yet longer CPU times.
Computational time becomes even longer when more complex chemistry (number of reactant species and/or number of participating reactions) and higher resolution reactor geometry are modeled. Computing time increases yet again if a transient solution is desired, when a pulsed process is investigated by simulation, or when a process is operating on multiple frequency scales, such as in the DF-CCP etching system. Multiple frequency scales or other multiple time based factors increase computational time because electron and ion transport properties within the plasma must be solved at both time scales. For example, the first frequency of the DF-CCP etching system can be 100 MHz (corresponding to a 10 ns time scale); and the second frequency can be 1-2 MHz (corresponding to a 1 μs time scale). Thus, the DF-CCP etching system must be solved for both the 10 ns and the 500 ns (or 1 μs) time scales. The computational time is related to the product of the number of iterations that each solution requires.
If the interactions between the ion flux and the processed wafer are considered, which can be over the time scale of several thousand RF cycles, the number of iterations and computational times can increase drastically.
Thus, there is a need to develop fast methods that would reduce computational real time in complex chemistry and geometry plasma systems. The fast algorithm and/or method could apply to solving numerically by finite elements modeling (FEM) methods, multiple frequency applications, pulsed plasma processes, sequential processing, contamination studies, feature profile evolutions, or developing industrial applications for etching or deposition technologies in plasmas.
Further, there is a need to develop and invent new, fast algorithms for technological plasma simulations and modeling. The simulation procedure should be practical and efficient for aiding in process and/or hardware development, for serving as an operational and predictive flexible tool, and for generating outputs as close as possible to the development needs and workflow in real time. Thousands of wafers are processed by the technological process on a daily basis, thus a large amount of experimental data related to hardware and software performance is readily available. Simulation procedures should be competitive in the rate of generating results to provide the ability to correlate, correct, or change the technological process in real time. This can represent large material and technical resource savings.